As compared to red wine technology, where pomace is macerated, the grape juices and musts are obtained by pressing the grapes and removing the pomace, thus removing an important source of antioxidant molecules. The objective of this study was to exploit the bioactive compounds from the black grape pomace and obtain a new food product, namely pasteurized red must with improved health-promoting properties. The study was conducted on four grape varieties for red wines—Fetească Neagră, Cabernet Sauvignon, Blauer Zweigelt, and Arcaș—each coming from a certain recognized Romanian vineyard, as follows: Murfatlar, Dealu Mare, Ștefănești-Argeș, and Iași, respectively. Both the must and the pomace extract used for each product were from the same variety and region. The recovery of polyphenols was achieved by macerating the pomace at ambient temperature, using solutions of ethanol in concentrations of 25%, 50%, and 75%. The results showed that the most efficient method of polyphenol recovery was obtained by using the ethanolic solution of 50%, which was selected for the subsequent stages of the study. The selected hydroalcoholic extract was concentrated by eliminating the solvent by roto evaporation and used as a source of supplementary bioactive compounds for the pasteurized must. The phenolic profiles of the musts enriched with phenolic extracts were determined by liquid chromatography, UHPLS-HRMS, revealing significant increases in the content of individual phenolic acids and other polyphenols. The phenolic extract recovered from the pomace significantly optimized the phenolic quality of the pasteurized must, thus contributing to the improvement of its nutritional value. The new product has a phenolic profile close to that of a red wine, but does not contain alcohol. Also, this technology is a sustainable method to convert grape waste into a safe, antioxidant-rich grape juice with potential health benefits.